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Improved FPT Algorithms for Weighted Independent Set in Bull-Free Graphs

  • Henri Perret du Cray
  • Ignasi SauEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)

Abstract

Very recently, Thomassé, Trotignon and Vušković [WG 2014] have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time \(2^{O(k^5)} \cdot n^9\). In this article we improve this running time to \(2^{O(k^2)} \cdot n^7\). As a byproduct, we also improve the previous Turing-kernel for this problem from \(O(k^5)\) to \(O(k^2)\). Furthermore, for the subclass of bull-free graphs without holes of length at most \(2p-1\) for \(p \ge 3\), we speed up the running time to \(2^{O(k \cdot k^{\frac{1}{p-1}})} \cdot n^7\). As \(p\) grows, this running time is asymptotically tight in terms of \(k\), since we prove that for each integer \(p \ge 3\), Weighted Independent Set cannot be solved in time \(2^{o(k)} \cdot n^{O(1)}\) in the class of \(\{bull,C_4,\ldots ,C_{2p-1}\}\)-free graphs unless the ETH fails.

Keywords

Parameterized complexity FPT algorithm Bull-free graphs Independent set Turing-kernel 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.AlGCo Project-team, CNRSLIRMMMontpellierFrance

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